So here’s that post:

Eddie: Would the same physicists all say that “the standard model is a true, or approximately true, depiction of nature?”

I don’t know about physicists.

As I see it, the standard model is neither true nor false as a depiction of nature. Our concept of “true” does not allow us to make such a judgment of the standard model.

Here’s the problem:

There is nothing at all that can be said directly about nature. In order to say something, we need words and we need a standard way of attaching those words to nature. Until we have the words and the standards, there is no basis for saying anything.

The role of the standard model is to provide us with those words and standards which would allow us to say things about nature. So the standard model, or some suitable replacement, is a prerequisite to being able to have true or approximately true depictions of nature.

I look at the cosmology of Genesis 1 in about the same way. In its time, it provided a vocabulary and a set of standards on how to have true depictions of nature. So I tend to see that cosmology as neither true nor false, but as setting the stage to be able to make true depictions. But, of course, it has been superseded by newer and better cosmologies.

In 1969, Eugene Wigner wrote what has become a famous paper, titled “The unreasonable effectiveness of mathematics in the natural sciences.” There’s a pretty good summary of the related issues in the Wikipedia article of the same name.

As you might guess from the title of this blog post, I disagree with Wigner. In my view, the effectiveness of mathematics is entirely reasonable. And it has long seemed reasonable to me. I thought about it either in high school or as a graduate student in mathematics (I’m not sure which), and came up with what I found to be a satisfactory explanation.

Perspective on mathematics

I’ll start with my broad perspective, which I have probably mentioned before on this blog. I often say that mathematics is not about reality. The mathematician Kronecker famously said “God gave us the natural numbers. All else is the work of man.” I almost agree, except that I think Kronecker gave God too much credit. As I see it, the natural numbers are also the work of man. That’s part of why I am a mathematical fictionalist.

In previous posts, I have discussed how we carve up the world, and how that carving up is what allows us to express true statements about the world. Science also expresses true statements about the world. In this post I will discuss how that relates to carving up.

Yes, science also carves up the world in its own way. And it does that in order to be able to make true statements about the world. So the basic idea is the same. But the method is very different.

Which science

Unsurprisingly, different sciences carve up the world in different ways. Biology is concerned with living organisms. So it wants to carve up the world into organisms, and then to further carve up those organisms into organs, cells, proteins, genes, etc. At a larger scale, it wants to look at populations of organism.

In this post, I shall mainly be looking at how physics carves up the world. That’s partly because the physics way of carving is most different from our ordinary way of carving. And, additionally, all sciences borrow from physics, at least to some extent.

Measuring

Take a look at a ruler, such as we use for measuring length. I have a ruler in front of me know, as I write this.

There’s a saying among mathematicians, that a topologist is someone who cannot tell the difference between a coffee cup and a donut. I’ll discuss that in this post, and I’ll suggest implications beyond mathematics.

Usually, when we say this, we are thinking of the donut and the coffee cup as two-dimensional surfaces. Once we go to the three-dimensional objects, nobody denies that the donut has a soft and spongy texture which makes it clearly different from a coffee cup.

Topology

Let’s start with a brief rundown on what is topology. It is a branch of mathematics where we discuss ideas such as continuity, convergence, etc. A classic example of convergence is with the sequence 0.9, 0.99, 0.999, … We can see that the sequence gets closer and closer to 1, and we say that it converges to 1. So topology has something to do with the geometric ideas of getting closer. But it does so without needing a notion of metric (or distance).

In an earlier post, I described the representation measurement of temperature. In this post, I describe the direct method. The contrast is intended to illustrate the distinction between representational theories of perception and direct theories of perception. By using an example from science (or perception written big), we illustrate in a way that is easier to see.

The design of the instrument

The design is almost the same as described in the earlier post. There is one addition. The mercury column in the capillary tube is directly calibrated in temperature. That is to say, there are graduation markings on the thermometer, from which we can directly read off the temperature.

As indicated in the previous post, I plan to use the measurement of temperature to illustrate some ideas about perception. This post will give a representationalist account of measurement, as an illustration of indirect perception.

The apparatus to be used is very similar to a mercury thermometer. I shall assume that the reader is reasonably familiar with traditional analog thermometers, and how they are used.

The design of the instrument

The thermometer uses a glass tube. At the bottom of the tube, there is a largish bulb which can be filled with mercury. Above the bulb, the glass tube contains only a very narrow tube of small diameter, sometimes called a capillary.

The bulb is initially filled with mercury, and the mercury extends to part way up the capillary tube. Above the mercury, the tube is empty. The air is pumped out, though it need not be a perfect vacuum.

Epistemology is a core area within philosophy. It is concerned with questions of knowledge, information, description and truth. And it is part of what I would like to see turned upside down. That is to say, the way that I see questions of knowledge, information, description and truth is very different from what we find in the traditional literature.

Epistemology from a design stance

As mentioned in my earlier “upside down” post, I see traditional philosophy as based on a design stance, while I would prefer a more evolutionary stance. So let’s start by looking at how the design stance seems to work.

While my title line might seem dramatic, I want to be clear that this post is not intended as a criticism of Kepler, or of Kepler’s laws. Rather, it is critical of the view that scientific laws are true descriptions of the world. This post is intended as part of my series on how science works. My aim is to describe my own understanding of Kepler’s laws.

The basis of Kepler’s laws

In case some of my readers are not familiar with them, Kepler’s laws are an attempt to account for the motion of the planets in our solar system. Kepler’s laws were preceded by the Ptolemaic idea that the planets moved in cycles and epicycles. Galileo argued, instead for the idea of Copernicus, that the planets traveled in circular paths around the sun. I presume that Kepler was looking for something a little more precise than the Copernican circles.

The tagline of coelsblog is “Defending Scientism” so it is no surprise that Coel is a proponent of scientism. However, his post also brings out some points on the nature of science, and that’s what I want to discuss here.

In earlier posts, I have preferred the Shannon notion of information, according to which information is a sequence of symbols. And I have emphasized that symbols are abstract objects. The symbols are usually considered to be intentional objects, because it is only on account of our intentions that we consider them to be symbols.

In this post, I want to relate the idea of symbol with that of category. I’ll start by assuming that the readers have at least an informal idea of what we mean by category.